Announcing the measures, Adam J Szubin, US acting under-secretary for terrorism and financial intelligence, said: “Iran’s ballistic missile programme poses a significant threat to regional and global security, and it will continue to be subject to international sanctions.”

However, Iranian foreign ministry spokesman Hossein Jaber Ansari said on Monday: “Iran’s missile programme has never been designed to be capable of carrying nuclear weapons.”

He said: “The US sanctions against Iran’s ballistic missile programme… have no legal or moral legitimacy.”

Mr Ansari added: “America sells tens of billions of dollars of weaponry each year to countries in the region. These weapons are used in war crimes against Palestinian, Lebanese and most recently Yemeni citizens.”

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Iranian Defence Minister Hossein Dehghan told the Fars news agency that the new US sanctions would have no effect.

He said: “We will prove it in practice by unveiling new missile achievements.”

A UN resolution endorsing the 2015 nuclear agreement between Iran and world powers calls on Iran to refrain from testing missiles designed to carry nuclear weapons.

On Saturday the International Atomic Energy Agency (IAEA) said it had verified that Iran had restricted its sensitive nuclear activities, as required by the agreement.

Four American-Iranians in Iran and seven Iranians in the US were also freed in a prisoner swap deal on the day sanctions were lifted.

The US had threatened to impose the missile test sanctions earlier but US sources said they were delayed as Washington did not want to undermine the negotiations over the nuclear deal, and in particular over the prisoner swap.

The sanctions were announced only after a plane carrying the released prisoners had left Iran.